A) \[{{\text{H}}^{\text{+}}}\] will be deflected most
B) \[{{\text{O}}^{\text{2}}}\] will be deflected most
C) \[H{{e}^{\text{2+}}}\]and \[{{\text{O}}^{\text{2-}}}\] will be deflected most
D) all will be deflected most
Correct Answer: A
Solution :
When a charged particle enters magnetic field perpendicularly, then it moves on circular path under magnetic force providing centripetal force. Magnetic force = centripetal force i.e. \[Bqv=\frac{m{{v}^{2}}}{r}\] or \[r=\frac{mv}{Bq}\] But \[E=\frac{1}{2}m{{v}^{2}}={{p}^{2}}/2m\] \[\therefore \] \[r=\frac{\sqrt{2ME}}{Bq}\] or \[r\propto \frac{\sqrt{m}}{q}\] \[\therefore \] \[{{r}_{{{H}^{+}}}}:{{r}_{H{{e}^{2+}}}}:{{r}_{{{O}^{2-}}}}=\frac{\sqrt{m}}{e}:\frac{\sqrt{4m}}{e}:\frac{\sqrt{16m}}{2e}\] \[=1:2:2\] Thus, \[H{{e}^{2+}}\]and\[{{O}^{2-}}\]are deflected equally while \[{{H}^{+}}\] is deflected most.You need to login to perform this action.
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